Taisne tx + 2y - 9 = 0 ir paralēla taisnei 24x - 4y + 3 = 0. Nosaki t skaitlisko vērtību. Otrās taisnes virziena koeficients k = Parametrs t =

Mathematical problem

The line tx + 2y - 9 = 0 is parallel to the line 24x - 4y + 3 = 0. Determine the numerical value of t.

The direction coefficient of the second line k =

Parameter t =

Solution:

• The general form of a linear equation is Ax + By + C = 0.
• For the first line, tx + 2y - 9 = 0, the coefficients are A1 = t, B1 = 2, C1 = -9.
• For the second line, 24x - 4y + 3 = 0, the coefficients are A2 = 24, B2 = -4, C2 = 3.
• Two lines are parallel if their slopes are equal. The slope (m) of a line in the form Ax + By + C = 0 is given by m = -A/B.
• Slope of the first line (m1) = -t/2.
• Slope of the second line (m2) = -24/(-4) = 6.
• Since the lines are parallel, m1 = m2.
• Therefore, -t/2 = 6.
• Multiplying both sides by 2, we get -t = 12.
• Multiplying by -1, we get t = -12.
• The direction coefficient k is the slope of the second line, which is m2 = 6.

Final Answer:

Parameter t = -12

The direction coefficient k = 6